Question: $g(x)=x^2+6x$ $h(x)=x^2-1$ Write $g(h(x))$ as an expression in terms of $x$. $g(h(x))=$
Answer: Let's write $h(x)$ as the input to function $g$. $g({h(x)})=({h(x)})^2+6({h(x)})$ Since $h(x)=x^2-1$, this becomes: $\begin{aligned} g({h(x)})&=({x^2-1})^2+6({x^2-1})\\ \\ &=x^4-2x^2+1+6x^2-6\\ \\ &=x^4+4x^2-5\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $g(h(x))=x^4+4x^2-5$